Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 5x + 3$ and $ JT = 4x + 12$ Find $CT$.
A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {5x + 3} = {4x + 12}$ Solve for $x$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 5({9}) + 3$ $ JT = 4({9}) + 12$ $ CJ = 45 + 3$ $ JT = 36 + 12$ $ CJ = 48$ $ JT = 48$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {48} + {48}$ $ CT = 96$